Once you've verified you have the correct version of the Dropbox app, you're ready to export to an SD card:

Tap the Quick Action button to the right of the filename you wish to export

Tap More

Tap Export

Tap Save to device

Select your external SD card

Note: If you do not see your external SD card listed:

After tapping Save to device, tap the Menu button

Tap Settings

Select Display advanced devices

You should see your external SD card appear as an export location

What happens when I export a file to a different app on my device?

When you choose to export a file to another application, the file is opened with the application selected. That application then handles the file. For example, if you've exported a file to the Gallery app on your device, that app will display the file but not actually store the file.